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Simplifying -3(1 + 7b) + 8(5n + 6) = 32 (1 * -3 + 7b * -3) + 8(5n + 6) = 32 (-3 + -21b) + 8(5n + 6) = 32 Reorder the terms: -3 + -21b + 8(6 + 5n) = 32 -3 + -21b + (6 * 8 + 5n * 8) = 32 -3 + -21b + (48 + 40n) = 32 Reorder the terms: -3 + 48 + -21b + 40n = 32 Combine like terms: -3 + 48 = 45 45 + -21b + 40n = 32 Solving 45 + -21b + 40n = 32 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -21b + -45 + 40n = 32 + -45 Reorder the terms: 45 + -45 + -21b + 40n = 32 + -45 Combine like terms: 45 + -45 = 0 0 + -21b + 40n = 32 + -45 -21b + 40n = 32 + -45 Combine like terms: 32 + -45 = -13 -21b + 40n = -13 Add '-40n' to each side of the equation. -21b + 40n + -40n = -13 + -40n Combine like terms: 40n + -40n = 0 -21b + 0 = -13 + -40n -21b = -13 + -40n Divide each side by '-21'. b = 0.619047619 + 1.904761905n Simplifying b = 0.619047619 + 1.904761905n
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